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Mar 5, 2019 at 13:51 history edited Olivier CC BY-SA 4.0
Corrected typo
Jul 8, 2014 at 18:22 comment added Olivier Ah! So the Weil-Deligne representation is not enough. Interesting.
Jul 8, 2014 at 6:44 comment added David Loeffler "In principle again, this describes completely $V(\rho_{f,p})$" -- not quite! You have to specify the filtration too. If $a_p$ is a non-unit then there is a unique possibility up to isomorphism. If $a_p$ is a unit, then there are two possibilities: the nontrivial filtration subspace can coincide with the non-unit Frobenius eigenspace, or it can be in general position, corresponding to the case where $\rho_{f, p}$ is a direct sum, or a non-split extension, of two characters.
Jul 8, 2014 at 6:02 comment added Olivier TL;DR David Loeffler's and Ricky's comments are spot on.
Jul 8, 2014 at 6:01 history answered Olivier CC BY-SA 3.0